The investigation of the intermolecular interactions between platinum-based anticancer drugs and lipid bilayers is of special relevance to unveil the mechanisms involved in different steps of the anticancer mode of action of these drugs. We have simulated the permeation of cisplatin through a model membrane composed of 1,2-dioleoyl-sn-glycero-3-phosphocholine lipids by means of umbrella sampling classical molecular dynamics simulations. The initial physisorption of cisplatin into the polar region of the lipid membrane is controlled, in a first moment, by long-range electrostatic interactions with the choline groups and, in a second step, by long-range electrostatic and hydrogen bond interactions with the phosphate groups. The second half of the permeation pathway, in which cisplatin diffuses through the nonpolar region of the bilayer, is characterized by the drop of the interactions with the polar heads and the rise of attractive interactions with the non-polar tails, which are dominated by van der Waals contributions.